In this paper, we introduce a discrete time-finite state model for pedestrian flow on a graph in the spirit of the Hughes dynamic continuum model. The pedestrians, represented by a density function, move on the graph choosing a route to minimize the instantaneous travel cost to the destination. The density is governed by a conservation law whereas the minimization principle is described by a graph eikonal equation. We show that the discrete model is well-posed and the numerical examples reported confirm the validity of the proposed model and its applicability to describe real situations.

A discrete hughes model for pedestrian flow on graphs / Camilli, Fabio; Festa, Adriano; Tozza, Silvia. - In: NETWORKS AND HETEROGENEOUS MEDIA. - ISSN 1556-1801. - STAMPA. - 12:1(2017), pp. 93-112. [10.3934/nhm.2017004]

A discrete hughes model for pedestrian flow on graphs

CAMILLI, FABIO;FESTA, ADRIANO;TOZZA, SILVIA
2017

Abstract

In this paper, we introduce a discrete time-finite state model for pedestrian flow on a graph in the spirit of the Hughes dynamic continuum model. The pedestrians, represented by a density function, move on the graph choosing a route to minimize the instantaneous travel cost to the destination. The density is governed by a conservation law whereas the minimization principle is described by a graph eikonal equation. We show that the discrete model is well-posed and the numerical examples reported confirm the validity of the proposed model and its applicability to describe real situations.
2017
Conservation law; Graph eikonal equation; Hughes model; Pedestrian flow; Well-posed discrete model; Statistics and Probability; Engineering (all); Computer Science Applications1707 Computer Vision and Pattern Recognition; Applied Mathematics
01 Pubblicazione su rivista::01a Articolo in rivista
A discrete hughes model for pedestrian flow on graphs / Camilli, Fabio; Festa, Adriano; Tozza, Silvia. - In: NETWORKS AND HETEROGENEOUS MEDIA. - ISSN 1556-1801. - STAMPA. - 12:1(2017), pp. 93-112. [10.3934/nhm.2017004]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/949588
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